Who’s Afraid of ANOVA? Dr. Ron Tibben-Lembke

Comparing Batteries Brand ObservationABC

Brand ObsABC Average = Count444

Sum of Squares  Compute average for each group  For each data point,  (data value – group average)^2  Sum these squared values

Sum of Squares Within Groups Brand ObsABC 1 ( ) 2 ( ) 2 ( ) 2 2 ( ) 2 (95-100) 2 ( ) 2 3 ( ) 2 ( ) 2 ( ) 2 4 ( ) 2 (82-100) 2 ( ) 2 SS11, =12,093

Sum of Squares-Total Brand ObsABC 1 ( ) 2 ( ) 2 ( ) 2 2 ( ) 2 ( ) 2 ( ) 2 3 ( ) 2 ( ) 2 ( ) 2 4 ( ) 2 ( ) 2 ( ) 2 SS338,61573,35892,012503,985

So Far:  Total Sum of Squares: 503,  Within Groups:12,093  Between Groups:

Computing F statistic  Total number of degrees of freedom = number of samples - 1 = 12-1 = 11  There are 3 groups, so ‘between groups’ Degrees of Freedom = 3 – 1 = 2  Within Groups DF = 11 – 2 = 9

Computing F statistic Source of Var. SSdfMSF Between491, , Within12, Total503,

Look up F critical Value

Significant?  Compare F statistic:  F critical value:  Yes! The difference is significant!  For alpha=0.01, Fcrit =  P value = 5.13x10 -8  = probability not significant